Transport in a long-range Kitaev ladder: Role of Majorana and subgap Andreev states

Abstract

We study the role of the constituent Majorana fermions and the subgap Andreev states on local and non-local transport across a two-leg long-range Kitaev ladder connected to metallic leads. The double degeneracy of Majorana fermions of the individual legs of the ladder gets lifted by a coupling between the two, resulting in the creation of Andreev bound states. A finite inter-leg hopping can be used to induce this coupling, provided a suitable superconducting phase difference (between the legs) is also applied. Andreev bound states formed strongly enhance local Andreev reflection. When the ladder and normal metal are weakly coupled the non-local nature of Andreev bound states enhances the non-local scattering weakly. When the ladder-normal metal interface is transparent to electron flow, we find that the subgap Andreev states enhance non-local conductance strongly. The features in the local and non-local conductances resemble the spectrum of the isolated ladder. Long-range pairing helps lift the degeneracy of the Majorana modes, makes them less localized, and thus inhibits local transport, while aiding non-local transport.